/**
 * NumberTricks demonstrates recursion-as-induction
 */
public class NumberTricks {
  
  /**
   * twelvePower returns the integer multiple of 11 that satisfies 12^n - 1 = 11k.
   * @param n the power to raise 12 to.
   * @return the integer multiple k of 11 so that 11k = 12^n - 1.
   */
  public static int twelvePower(int n) {
    if (n == 0) {
      return 0;
    }
    else {
      return 12 * twelvePower(n - 1) + 1;
    }
  }
  
}